8 comments:

Seriously thinking about your arguments. I not a catholic but I love listening to thinking catholics. I am based in the UK and I hope I can find a place to watch The Principle in the near future. Best Wishes (apologies if this isn't a catholic expression).

Welcome, Liebniz Zero ( a very fascinating internet moniker by the way- I wonder if it refers to the actual infinitesimal in the Liebniz calculus, or whether- please God forbid!- this is a statement of the value you place on the genius Liebniz' work)!

I sincerely hope and expect you will be able to view "The Principle" by the end of this year in the UK, either theatrically or else via VOD or DVD.

Even Catholics appreciate the best wishes of their well-spoken interlocutors!

Thanks, Mr Delano, for your welcome. I am tempted to put a 'smiley' or 'lol' here! The moniker 'Leibnitz One' was already taken, but as one cannot go anywhere without knowing where the Origin is - 'Leibnitz Zero' seemed the second best option!

Let me ask you three questions.

1). Does it bother you that Newton's First Law equates Linear Zero acceleration with zero velocity; while the 'Equations of (Linear 2D Kinematic) Motion' only have meaning when the acceleration is a constant throughout the whole of the time-period?

2). Does it bother you that the application of a force can have nothing to do with mass; as in a magnetic field?

3) Only transverse waves can support polarization , leading to rejection of longitudinal modes by the EM pioneers .... but EM waves propagate through aether by causing a longitudinal aether disturbance ...which is probably what Tesla et al measured...... So, this is no bother.

The point I was hoping to discuss, in a friendly way, was how arc-length displacement is not linear displacement; nor is it angular displacement. Studying, what are the four (x2) equations of linear & rotational kinematic motion, (i.e., movement without reference to forces), arc-length displacement (s) seems to have been equated with linear displacement (x). The variables of the four equations of linear motion are: initial linear velocity (u), final linear velocity (v), time (t), linear displacement (x), acceleration (a) and average mean velocity (v-bar); Within the time-period (t), the acceleration (a) must remain a constant.The variables of the four equations of rotational motion are: initial angular velocity (ω subscript 0 (for want of a better font)), final angular velocity (ω subscript 1), time (t), angular displacement (θ), angular acceleration (α) and the average mean angular velocity (ω-bar); Within the time-period (t), the angular acceleration (α) must remain a constant.When claiming conversion from a linear to a rotational description, and vice versa, textbooks write: x = rθ , declaring the righthand side equal to linear displacement, as contained in the four equations of linear motion. The product rθ (radius × angular displacement) is an arc-length displacement, having the qualities of: magnitude, positive or negative angular direction, and the ability to totally orientate itself in space without requiring an external coordinate system. This is because it defines a unique point elsewhere, i.e, the centre of the arc at the other end of the radius. This is not linear displacement (x). A straight line segment, without a person envisioning it shrunk or stretched in any way, can be viewed to be any length - other than infinitely large or infinitely small - because its 'length' is a representation, not an intrinsic quality. The 'length' can only be derived from the context of its environment. The scale of the straight-line segment's environment is what defines its 'length'. At least one external point in its two dimensional environment has to be also given for the straight-line segment to be oriented, setting up a Pythagorean triangle in Euclidean geometry.In a sense, progressive arc-length displacement produces its own environment, and at any moment, its place in that environment, as it is being produced.Angular displacement (θ) is merely facing different directions from a single point, without journeying, so to speak.I think most of us have been conditioned to see θ as an arc length. But it is not, it is a change of direction-facing on/at the same point. Angular displacement (θ) can be seen as the ratio (or equivalence relation) between an arc-length displacement and its radius, i.e. θ = s/r. An equivalence relation is dimensionless. Theta (θ) does not tell us how big the radius with its arc length is - they both could be infinitely large or infinitely small - but the dimensionless relation theta (θ) would still meaningfully give the equivalence relation between the two. But a progressive change in arc-length displacement, if the original point of production is not forgotten over time, does record its own history as it develops. Hence, the rate of change of arc-length displacement (ds/dt) tells you more than the rate of change of angular displacement (dθ/dt), AND it tells you more than the rate of change of instantaneous linear tangential velocity, dx/dt, i.e., u or v.The rate of change of arc-length displacement is not angular velocity ω, and it is not the instantaneous tangential linear velocity, v or u.So, after making my thoughts explicit to myself, I am saying, at the moment, that there has been an oversight at the root of describing movement, ds/dt ≠ dx/dt, x ≠ rθ, as s = rθ, i.e, s ≠ x in the linear/rotational kinematic equations.If anything I have written is false please put me right. If what I have written seems inconsequential to you, I can live with that.